If V={(x,y)|x,y ∈ R} with acts (x1,y1)@(x2,y2)=(3√(x13+x23),3√(y13+y23)) and a$(x1,y1)=(ax1,ay1) , a ∈ R.
Prove V with this acts is NOT vector space.Thank you!
are you sure it's not?
it's addition has commutativity and associativity
(0,0) is the clear additive identity and (-x,-y) is the additive inverse of (x,y)
the scalar properties are identical to the Euclidean vector space
I'm not seeing why this isn't a vector space.
remember the cube and cube root form a bijection
This is not a vector space. Exactly one of the axioms of a vector space is not satisfied.
Rom yes im sure the exercise say it's not.For this reason i can't solve the exercise
Guest "Exactly one of the axioms of a vector space is not satisfied"
Witch is this axiom?